“What you saw there is very close to what we’ll actually build,” Mr. Musk said, referring to the rockets and spacecraft in the video.

Mr. Musk estimated it would cost $10 billion to develop the rocket, and he said the first passengers to Mars could take off as soon as 2024 if the plans went off without a hitch. For now, SpaceX is financing development costs of a few tens of millions of dollars a year, but eventually the company would look to some kind of public-private partnership.

Each of the SpaceX vehicles would take 100 passengers on the journey to Mars, with trips planned every 26 months, when Earth and Mars pass close to each other. Mr. Musk said the first flights would be “fairly expensive” but ticket prices might eventually fall to between $100,000 and $200,000 a person.

To establish a self-sustaining Mars civilization of a million people would take 10,000 flights, with many more to ferry equipment and supplies.

“We’re going to need something quite large to do that,” Mr. Musk said. It would take 40 years to a century before the city on Mars became self-sufficient, he said.

The mood at the conference was almost as giddy as a rock concert or the launch of a new Apple product, with people lining up for Mr. Musk’s presentation a couple of hours in advance.

Mr. Musk has talked of his “Mars Colonial Transporter,” but a couple of weeks ago, he suggested that its capabilities would be much greater.

He now calls it the Interplanetary Transport System. The booster would include 42 of SpaceX’s new, more powerful Raptor engines. On Monday, he posted an image on Twitter of the first testing of a Raptor.

Mars has long been the goal of Mr. Musk and SpaceX.

Much of Mr. Musk’s initial wealth came from his tenure as chief executive of PayPal, which was sold to eBay in 2002 for $1.5 billion. Afterward, he wanted to undertake a science experiment — to send a greenhouse to Mars and see if Earth plants could grow in Martian dirt. He said the rocket options for launching his project were so lacking that he started SpaceX, which has headquarters in Hawthorne, Calif.

SpaceX has established a successful business with its workhorse Falcon 9 rocket launching satellites, and by taking cargo — and soon astronauts — to the International Space Station for NASA. But Mr. Musk has stated often that his loftier goal for SpaceX is to send people to Mars to make humanity a “multiplanetary species” in order to ensure survival in case some calamity like an asteroid strike befell Earth.

The new rocket could be used for even more distant trips, to places like Europa, the icy moon of Jupiter.

“This system really gives you freedom to go anywhere you want in the greater solar system,” he said.

What is less clear is how SpaceX will raise the money needed to bring its Mars dreams to fruition. The new rocket is by far the largest ever.

Scott Pace, a former NASA official who is the director of the Space Policy Institute at George Washington University, said Mr. Musk’s vision was plausible technically, but added, “Other than emotional appeal, however, it didn’t really address why governments, corporations or other organizations would fund the effort.” His bottom-line opinion: “Possible, but not probable.”

During his talk, Mr. Musk put up a slide titled “Funding.” The first item was “Steal underpants,” a joking reference to a “South Park” episode. He also listed SpaceX’s businesses — launching satellites and sending NASA cargo and astronauts to the space station — and “Kickstarter.”

But he admitted that SpaceX would probably not be able to do it alone. “Ultimately, this is going to be a huge public-private partnership,” he said.

SpaceX has received much of the financing for its rocket development from NASA, from contracts to take cargo to and from the International Space Station. The United States Air Force is providing $33.6 million for development of the Raptor.

Critics of SpaceX and Mr. Musk question whether the Mars dreams are distracting the company from its more mundane business. SpaceX’s Falcon 9 rocket is grounded while investigators try to figure out why one of the rockets on the launchpad exploded this month during fueling before a test firing.

On Friday, the company said the failure appeared to be a large breach in the helium system of the second stage, although what caused the breach is not known. However, the company said the investigation had ruled out any connection to the failure last year of a Falcon 9 that disintegrated in flight. (That failure was traced to a faulty strut in the second stage, and SpaceX resumed launching later in the year.)

Mr. Musk also faces competition from other billionaires with ambitious space dreams. Jeff Bezos, the founder of Amazon, has his own rocket company, Blue Origin, which this month also announced a new rocket, New Glenn, that approaches the Saturn 5 in stature, but is dwarfed by SpaceX’s new rocket.

At a talk here, Robert Meyerson, Blue Origin’s president, said the aim of New Glenn was to take people to space, although it will also be able to launch satellites. The images the company released showed the satellite-carrying version. But Mr. Meyerson disclosed that “there are other versions that will have a space vehicle on top.”

Mr. Meyerson said Blue Origin had an even larger rocket, to be called New Armstrong, on the drawing board. Mr. Bezos has said his goal is for millions of people to live in space, although he has not mentioned Mars as a destination.

With Mr. Bezos’ Amazon wealth, Blue Origin faces less pressure to be profitable as quickly as SpaceX, or public companies like Boeing and Lockheed Martin that have to answer to shareholders.

NASA is still talking about its Mars ambitions, too, and its own giant rocket, the Space Launch System, for eventual human missions there. William H. Gerstenmaier, the associate administrator for human exploration and operations, said all of the pieces for a crewed Mars mission were in development, at least to reach Mars orbit, by the 2030s and fit within the agency’s existing budget. “We don’t think we’re going to get a big new budget,” he said.

He admitted that in NASA’s plans, astronauts’ setting foot on Mars would take longer, probably not until the 2040s.

Mr. Musk was confident that his company could pull off his vision, but he said he would not be among the first colonists, saying he wants to see his children grow up. The chances of dying on that first trip to Mars, he said, are “quite high.”

Correction:Nov. 2, 2016

An article on Sept. 28 about Space X’s plans to send humans to Mars paraphrased incorrectly from comments by Elon Musk, founder of Space X, about the cost of future flights. He said only that initial prices would be fairly expensive — not that they would initially cost $500,000. (Mr. Musk said the aim would be for ticket prices to fall to less than $200,000.) The article also referred imprecisely to Mr. Musk’s relationship with PayPal when it was acquired by eBay. While he was still a board member and made money from the sale, he was not PayPal’s C.E.O. at the time and he did not sell it to eBay. This correction was delayed because editors did not follow through when the errors were pointed out.

A version of this article appears in print on , Section A, Page 10 of the New York edition with the headline: Billionaire Unveils Plan to Take Humans to Mars as Early as 2024. Order Reprints | Today’s Paper | Subscribe